Download Predator-prey-code

The hare birth rate is constant, as their food supply is
unlimited. Hares only die when eaten by a lynx, and the
number of hares eaten is proportional to how often hares
& lynxes meet, i.e., the chance of a lynx catching a hare.
The lynx birth rate is also proportional to how often hares
& lynxes meet, i.e., the food available for each lynx family.
Lynxes only die from natural causes, and their death rate is
constant.
Computational Thinking
Relevant
input
Automation
Abstraction
Problem description
Computational goal
Information extraction
Algorithm design
Algorithm implementation
Recipe (Algorithm)
Answer
1. Generate population data.
a.
Repeatedly, generate next population.
2. Display population data.
Given ℎ0 , 𝑙0 , ℎ𝑎𝑟𝑒𝐵𝑖𝑟𝑡ℎ, ℎ𝑎𝑟𝑒𝑃𝑟𝑒𝑑𝑎𝑡𝑖𝑜𝑛, 𝑙𝑦𝑛𝑥𝐵𝑖𝑟𝑡ℎ,
𝑙𝑦𝑛𝑥𝐷𝑒𝑎𝑡ℎ, 𝑦𝑒𝑎𝑟𝑠.
Repeat these steps for 𝑦 = 0, … , 𝑦𝑒𝑎𝑟𝑠 − 1:
ℎ𝑦+1 = ℎ𝑦 + ℎ𝑦 ∙ ℎ𝑎𝑟𝑒𝐵𝑖𝑟𝑡ℎ − ℎ𝑎𝑟𝑒𝑃𝑟𝑒𝑑𝑎𝑡𝑖𝑜𝑛 ∙ 𝑙𝑦
𝑙𝑦+1 = 𝑙𝑦 + 𝑙𝑦 ∙ 𝑙𝑦𝑛𝑥𝐵𝑖𝑟𝑡ℎ ∙ ℎ𝑦 − 𝑙𝑦𝑛𝑥𝐷𝑒𝑎𝑡ℎ
Plot 𝑦, ℎ𝑦 for 𝑦 = 0, … , 𝑦𝑒𝑎𝑟𝑠.
Plot 𝑦, 𝑙𝑦 for 𝑦 = 0, … , 𝑦𝑒𝑎𝑟𝑠.
Improve Algorithm
• Separate parts
• Generalize
• Articulate goals
1. Generate population data.
a.
Repeatedly, generate next population.
2. Display population data.
Given ℎ0 , 𝑙0 , ℎ𝑎𝑟𝑒𝐵𝑖𝑟𝑡ℎ, ℎ𝑎𝑟𝑒𝑃𝑟𝑒𝑑𝑎𝑡𝑖𝑜𝑛, 𝑙𝑦𝑛𝑥𝐵𝑖𝑟𝑡ℎ,
𝑙𝑦𝑛𝑥𝐷𝑒𝑎𝑡ℎ, 𝑦𝑒𝑎𝑟𝑠.
Repeat these steps for 𝑦 = 0, … , 𝑦𝑒𝑎𝑟𝑠 − 1:
ℎ𝑦+1 = ℎ𝑦 + ℎ𝑦 ∙ ℎ𝑎𝑟𝑒𝐵𝑖𝑟𝑡ℎ − ℎ𝑎𝑟𝑒𝑃𝑟𝑒𝑑𝑎𝑡𝑖𝑜𝑛 ∙ 𝑙𝑦
𝑙𝑦+1 = 𝑙𝑦 + 𝑙𝑦 ∙ 𝑙𝑦𝑛𝑥𝐵𝑖𝑟𝑡ℎ ∙ ℎ𝑦 − 𝑙𝑦𝑛𝑥𝐷𝑒𝑎𝑡ℎ
Plot 𝑦, ℎ𝑦 for 𝑦 = 0, … , 𝑦𝑒𝑎𝑟𝑠.
Plot 𝑦, 𝑙𝑦 for 𝑦 = 0, … , 𝑦𝑒𝑎𝑟𝑠.
Given ℎ0 , 𝑙0 , ℎ𝑎𝑟𝑒𝐵𝑖𝑟𝑡ℎ, ℎ𝑎𝑟𝑒𝑃𝑟𝑒𝑑𝑎𝑡𝑖𝑜𝑛, 𝑙𝑦𝑛𝑥𝐵𝑖𝑟𝑡ℎ,
𝑙𝑦𝑛𝑥𝐷𝑒𝑎𝑡ℎ, 𝑦𝑒𝑎𝑟𝑠.
Repeat these steps for 𝑦 = 0, … , 𝑦𝑒𝑎𝑟𝑠 − 1:
ℎ𝑦+1 = ℎ𝑦 + ℎ𝑦 ∙ ℎ𝑎𝑟𝑒𝐵𝑖𝑟𝑡ℎ − ℎ𝑎𝑟𝑒𝑃𝑟𝑒𝑑𝑎𝑡𝑖𝑜𝑛 ∙ 𝑙𝑦
𝑙𝑦+1 = 𝑙𝑦 + 𝑙𝑦 ∙ 𝑙𝑦𝑛𝑥𝐵𝑖𝑟𝑡ℎ ∙ ℎ𝑦 − 𝑙𝑦𝑛𝑥𝐷𝑒𝑎𝑡ℎ
Return 𝒉 and 𝒍.
Why Separate Parts?
• Simpler
• Independently useful
Generalize beyond Hares & Lynxes
Given 𝑝𝑟𝑒𝑦0 , 𝑝𝑟𝑒𝑑0 , 𝑔𝑟𝑜𝑤𝑡ℎ, 𝑝𝑟𝑒𝑑𝑎𝑡𝑖𝑜𝑛, 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛,
𝑑𝑒𝑎𝑡ℎ, 𝑦𝑒𝑎𝑟𝑠.
Repeat these steps for 𝑦 = 0, … , 𝑦𝑒𝑎𝑟𝑠 − 1:
𝑝𝑟𝑒𝑦𝑦+1 = 𝑝𝑟𝑒𝑦𝑦 + 𝑝𝑟𝑒𝑦𝑦 ∙ 𝑔𝑟𝑜𝑤𝑡ℎ − 𝑝𝑟𝑒𝑑𝑎𝑡𝑖𝑜𝑛 ∙
Articulate Goals
Populations:
Given 𝑝𝑟𝑒𝑦0 , 𝑝𝑟𝑒𝑑0 , 𝑔𝑟𝑜𝑤𝑡ℎ, 𝑝𝑟𝑒𝑑𝑎𝑡𝑖𝑜𝑛, 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛, 𝑑𝑒𝑎𝑡ℎ,
𝑦𝑒𝑎𝑟𝑠.
Returns the predicted populations of two species, given their
initial populations, the prey’s growth rate, the predation rate,
the predator’s food conversion rate, the predator’s death rate,
and the number of years to predict.
Repeat these steps for 𝑦 = 0, … , 𝑦𝑒𝑎𝑟𝑠 − 1:
𝑝𝑟𝑒𝑦𝑦+1 = 𝑝𝑟𝑒𝑦𝑦 + 𝑝𝑟𝑒𝑦𝑦 ∙ 𝑔𝑟𝑜𝑤𝑡ℎ − 𝑝𝑟𝑒𝑑𝑎𝑡𝑖𝑜𝑛 ∙ 𝑝𝑟𝑒𝑑𝑦
𝑝𝑟𝑒𝑑𝑦+1 = 𝑝𝑟𝑒𝑑𝑦 + 𝑝𝑟𝑒𝑑𝑦 ∙ 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 ∙ 𝑝𝑟𝑒𝑦𝑦 − 𝑑𝑒𝑎𝑡ℎ
Return 𝑝𝑟𝑒𝑦 and 𝑝𝑟𝑒𝑑.
Express as Python Code
Use What Kinds of Python Data?
Populations:
Given 𝑝𝑟𝑒𝑦0 , 𝑝𝑟𝑒𝑑0 , 𝑔𝑟𝑜𝑤𝑡ℎ, 𝑝𝑟𝑒𝑑𝑎𝑡𝑖𝑜𝑛, 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛, 𝑑𝑒𝑎𝑡ℎ,
𝑦𝑒𝑎𝑟𝑠.
Returns the predicted populations of two species, given their
initial populations, the prey’s growth rate, the predation rate,
the predator’s food conversion rate, the predator’s death rate,
and the number of years to predict.
Repeat these steps for 𝑦 = 0, … , 𝑦𝑒𝑎𝑟𝑠 − 1:
𝑝𝑟𝑒𝑦𝑦+1 = 𝑝𝑟𝑒𝑦𝑦 + 𝑝𝑟𝑒𝑦𝑦 ∙ 𝑔𝑟𝑜𝑤𝑡ℎ − 𝑝𝑟𝑒𝑑𝑎𝑡𝑖𝑜𝑛 ∙ 𝑝𝑟𝑒𝑑𝑦
𝑝𝑟𝑒𝑑𝑦+1 = 𝑝𝑟𝑒𝑑𝑦 + 𝑝𝑟𝑒𝑑𝑦 ∙ 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 ∙ 𝑝𝑟𝑒𝑦𝑦 − 𝑑𝑒𝑎𝑡ℎ
Return 𝑝𝑟𝑒𝑦 and 𝑝𝑟𝑒𝑑.
𝑝𝑟𝑒𝑦 and 𝑝𝑟𝑒𝑑 as Lists
𝑝𝑟𝑒𝑦 = 𝑝𝑟𝑒𝑦0 𝑝𝑟𝑒𝑦1 𝑝𝑟𝑒𝑦2 𝑝𝑟𝑒𝑦3 𝑝𝑟𝑒𝑦4
…
𝑝𝑟𝑒𝑑 = 𝑝𝑟𝑒𝑑0 𝑝𝑟𝑒𝑑1 𝑝𝑟𝑒𝑑2 𝑝𝑟𝑒𝑑3 𝑝𝑟𝑒𝑑4
…
Translate Piece by Piece
Populations:
Given 𝑝𝑟𝑒𝑦0 , 𝑝𝑟𝑒𝑑0 , 𝑔𝑟𝑜𝑤𝑡ℎ, 𝑝𝑟𝑒𝑑𝑎𝑡𝑖𝑜𝑛, 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛, 𝑑𝑒𝑎𝑡ℎ,
𝑦𝑒𝑎𝑟𝑠.
Returns the predicted populations of two species, given their
initial populations, the prey’s growth rate, the predation rate,
the predator’s food conversion rate, the predator’s death rate,
and the number of years to predict.
def populations(prey0,pred0,growth,predation,conversion,death,years):
"""Returns the predicted populations of two species, given their
initial populations, the prey's growth rate, the predation
rate, the predator's food conversion rate, the predator's
death rate, and the number of years to predict."""
prey = [prey0]
pred = [pred0]
Translate Piece by Piece
Repeat these steps for 𝑦 = 0, … , 𝑦𝑒𝑎𝑟𝑠 − 1:
for y in range(years):
Translate Piece by Piece
𝑝𝑟𝑒𝑦𝑦+1 = 𝑝𝑟𝑒𝑦𝑦 + 𝑝𝑟𝑒𝑦𝑦 ∙ 𝑔𝑟𝑜𝑤𝑡ℎ − 𝑝𝑟𝑒𝑑𝑎𝑡𝑖𝑜𝑛 ∙ 𝑝𝑟𝑒𝑑𝑦
𝑝𝑟𝑒𝑑𝑦+1 = 𝑝𝑟𝑒𝑑𝑦 + 𝑝𝑟𝑒𝑑𝑦 ∙ 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 ∙ 𝑝𝑟𝑒𝑦𝑦 − 𝑑𝑒𝑎𝑡ℎ
prey.append( prey[y] + prey[y] * (growth-predation*pred[y]) )
pred.append( pred[y] + pred[y] * (conversion*prey[y]-death) )
Translate Piece by Piece
Return 𝑝𝑟𝑒𝑦 and 𝑝𝑟𝑒𝑑.
return prey , pred
Put the Function’s Pieces Together
def populations(prey0,pred0,growth,predation,conversion,death,years):
"""Returns the predicted populations of two species, given their
initial populations, the prey's growth rate, the predation
rate, the predator's food conversion rate, the predator's
death rate, and the number of years to predict."""
prey = [prey0]
pred = [pred0]
for y in range(years):
prey.append(prey[y] + prey[y] * (growth-predation*pred[y]))
pred.append(pred[y] + pred[y] * (conversion*prey[y]-death))
return prey, pred
How to Use The Code?
pred, prey = populations(100,50,.4,.003,.004,.2,10)
A Useful Aside
def populations(prey0,pred0,growth,predation,conversion,death,years):
"""Returns the predicted populations of two species, given their
initial populations, the prey's growth rate, the predation
rate, the predator's food conversion rate, the predator's
death rate, and the number of years to predict."""
prey = [prey0]
pred = [pred0]
for y in range(years):
print "y = ", y
print "prey = ", prey
print "pred = ", pred
prey.append(prey[y] + prey[y] * (growth-predation*pred[y]))
pred.append(pred[y] + pred[y] * (conversion*prey[y]-death))
return prey, pred
Plotting
import matplotlib.pyplot as plt
def plotPopulations(times,prey,pred,preyName,predName):
"""Displays a plot of two populations over the given times."""
# Prey use circles connected by solid line.
preyPlot = plt.plot(times, prey, 'o-' )
# Predators use squares connected by dotted line.
predPlot = plt.plot(times, pred, 's:' )
# Place legend box in "best" location.
plt.legend((preyPlot, predPlot), (preyName, predName), 'best')
plt.xlabel('Years')
plt.ylabel('Population')
plt.title('Predator-Prey Model')
plt.show()
Putting Everything Together
import matplotlib.pyplot as plt
def populations(…):
…
def plotPopulations(…):
…
prey, pred = populations(100,50,.4,.003,.004,.2,10)
times = range(len(prey))
plotPopulations(times,prey,pred,"Hare","Lynx")